In your second example we have a perífrasis verbal.
According to the DRAE
- f. Gram. Unidad predicativa constituida generalmente por un verbo auxiliar en forma personal y un verbo auxiliado en forma no personal
[English: Predicative unit generally formed by an auxiliary verb in personal form and a main verb in non-personal form.
Notice that I have "translated" auxiliado by main, applying the definition of auxiliary that appears in the Cambridge Dictionary
auxiliary verb: a verb that gives grammatical information not given by the main verb of a sentence
The main verb of a "perífrasis verbal" is always in non-personal form meaning that it's an infinitive, a gerund or a participle. It's always the auxiliary verb, poder in your case, the one that applies person, number and genre.
Notice that the same occurs in English with the verb can that you quoted. This verb is a modal verb and
Modal verbs (can, could, may, might, will, shall, would, should and must) are followed by a bare infinitive source
More info [in Spanish] about "perífrasis verbales" here.